## Math Caching and Immediately Useful Teaching Data

Last July, I posted a video in which I showed how to create a local, customized version of the Math Caching activity that can be found here.

I was inspired to revisit the idea last weekend reading Dan Meyer’s post about teacher dashboards. The part that got me thinking, and that stoked the fire that has been going in my head for a while, is identifying the information that is most useful to teachers. There are common errors that an experienced teacher knows to expect, but a new teacher may not recognize is common until it is too late. Getting a measure of wrong answers, and more importantly, the origin of those wrong answers, is where we ideally should be making the most of the technology in our (and the students’) hands. Anything that streamlines the process of getting a teacher to see the details of what students are doing incorrectly (and not just that they are getting something wrong) is valuable. The __only__ way I get this information is by looking at student work. I need to get my hands on student responses as quickly as I can to make sense of what they are thinking.

As we were closing in on the end of an algebra review unit with the ninth graders this week, I realized that the math cache concept was good and fun and at a minimum was a remastering of the review sheet for a one-to-one laptop classroom. I came up with a number of questions and loaded it into the Python program. When one of my Calculus students stopped in to chat, and I showed her what I had put together, I told her that I was thinking of adding a step where students had to upload a screenshot of their written work in addition to entering their answer into the location box. She stared at me and said blankly: ‘You absolutely have to do that. They’ll cheat otherwise.’

While I was a bit more optimistic, I’m glad that I took the extra time to add an upload button on the page. I configured the program so that each image that was uploaded was also labeled with the answer that the student entered into the box. This way, given that I knew what the correct answers were, I knew which images I might want to look at to know what students were getting wrong.

This was pure gold.

Material like this was quickly filling up the image directory, and I watched it happening. I immediately knew which students I needed to have a conversation with. The answers ranged from ‘no solution’ to ‘identity’ to ‘x = 0’ and I instantly had material to start a conversation with the class. Furthermore, I didn’t need to throw out the tragically predictable ‘who wants to share their work’ to a class of students that don’t tend to want to share for all sorts of valid reasons. I didn’t have to cold call a student to reluctantly show what he or she did for the problem. I had their work and could hand pick what I wanted to share with the class while maintaining their anonymity. We could quickly look at multiple students’ work and talk about the positive aspects of each one, while highlighting ways to make it even better.

In this problem, we had a fantastic discussion about communicating both reasoning and process:

The next step that I’d like to make is to have this process of seeing all of the responses be even more transparent. I’d like to see student work popping up in a gallery that I can browse and choose certain responses to share with the class. Another option to pursue is to get students seeing the responses of their peers and offer advice.

Automatic grading certainly makes the job of answering the right/wrong question much easier. Sometimes a student does need to know whether an answer is correct or not. Given all the ways that a student could game the system (some students did discuss using Wolfram Alpha during the activity) the informative part on the teaching and assessment end is seeing the work itself. This is also an easy source of material for discussion with other teachers about student work (such as with Michael Pershan’s Math Mistakes).

I was blown away with how my crude hack to add this feature this morning made the class period a much richer opportunity to get students sharing and talking about their work. Now I’m excited to work on the next iteration of this idea.